Indexability and Index Heuristics for a Simple Class of Inventory Routing Problems
成果类型：
Article
署名作者：
Archibald, T. W.; Black, D. P.; Glazebrook, K. D.
署名单位：
University of Edinburgh; Lancaster University
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1070.0505
发表日期：
2009
页码：
314-326
关键词：
摘要：
We utilise and develop Whittle's restless bandit formulation to analyse a simple class of inventory routing problems with direct deliveries. These routing problems arise from the practice of vendor-managed inventory replenishment and concern the optimal replenishment of a collection of inventory holding locations controlled centrally by a decision maker who is able to monitor inventory levels throughout the network. We develop a notion of location indexability from a Lagrangian relaxation of the problem and show that (subject to mild conditions) the locations are indeed indexable. We thus have a collection of location indices in closed form, namely, real-valued functions of the inventory level (one for each location), which measure in a natural way (namely, as a fair charge for replenishment) each location's priority for inclusion in each day's deliveries. We discuss how to use such location indices to construct heuristics for replenishment and assess a greedy index heuristic in a numerical study where it performs strongly. A simpler approximate index analysis is available for the case in which the demand at each location is Poisson. This analysis permits a more explicit characterisation of the range of holding cost rates for which (approximate) location indexability is guaranteed.